i  ^^ 

L747 


UC-NRLF 


B  3  ma  7m 


V     *" 


■i 


^-^               /-           Cf^ 

(1^ 

V 

DIAGNOSTIC  TEoTS   OF  ABILITY  TO  ADD   IIITEGERS. 


By 


RUDOLPH,    LIiroQUIST 


THESIS 


Submitted  in  partial  satisfaction  •f  the  requirements  f«r  the  degree  •f 


llASTER  OF  ARTS 


EDUG.VriON 

in 

the 

GRADUATE 

DIVISION 

of 

the 

HIWIRSITY  ( 

3F  CALIFORNIA 

Dec« 

1922. 

9-.  !a/'  f/^'T 


Digitized  by  the  Internet  Arciiive 

in  2008  with  funding  from 

IVIicrosoft  Corporation 


http://www.archive.org/details/diagonstictestsoOOIindrich 


PART   ONE 

INTKODIIGTORY   STATFl/ff-^NT 

Tills   study    la    Intended    to  rer.ult    in   tho    constr-uctlon 
of   a  raeaHui'lng  devlco   by  mcfine,    of  v/hlcVi  the    teacher   will   be   able 
to  determino   the  particular  .addition  habltt, ,    the   dovolopinent   of 
whlcVi  reodti    to   be   emphaslzod  wltli  her  cIhsb. 

The   t^rowth    of    the    teat   raovt-iiifiit.    huti    ti'un   a    ti't)i.u;ndoua 
Increase    in   the   number  of    teats,    but    It   aeoins    Uiat  fiuffjolont 
ernphat'.j  h   has   not    been   placed   upon   tl-ie   development   oi'    tho&e    that 
are   of  dlatsnoatlc,   rather    than  general    value,      'i'he    teacher  needs 
to   know,    not    only,    how  i^i-t)ut    la    the   general   ability   of   hei-  class 
or    of   a    r»r^'l-t;uiMr    individual,    but   altio,    in  ceat)    they    are    not  as 
goo(]   aa    they  thould   be,    tVie  particular  habita    t}u>  t  are   undevelop- 
ed. 

All  testa    are    in  some   sense    or   to  aoiae   degree   diagnos- 
tic.     Even  aueyi   afl    teat  as    the   Courtia   L>tandard  Researcyi   Tests 
altVioui^h   they   werti   not    iaaued    aa    definitely   diagnostic   teatfi   are 
Bucli    lo   the   extent   to  wlil  ch   they   enable    the   teaclier'   to  cUaermine 
whijch   <jf   tlie  f(XAr   IVuidamontul   operations   her   clt'St^    has   moat  need 
to   work   up(.;n.      Tliey    enable    a    teacher    to   know    v/h  ether  or   not    her 
clasfi    cwi   do    thr-ee    liy    nine    /uld]  tlon  as    well    as    they    can   do   two 
by   four  iiiulti|jll  cation  or    two    by    five    diviaion,    but    they   give 
her  no  Vie].])    in   duoltUng,    in    l.he    caae;    of   aiMltluti,    w>iother    or 
not    it   lb    addition  corablnatlona,    as   such,    that   tl-ie   children 

are   hf.iV\nR    troiible    with  or  wheUier    it   is   carr-ying,    or   wViether 

"440  0  1* 


.X. 


'    '    ■  '   '  -  ■  ■•      •■  ■  '   "       I  i  ■■     .i/  ■•>.       !•,  ,  I  I  n  III      n  I  li  I  11,   I  ■  il  L  . 


Page   2. 


General    tests,    such  as   Vioody-McCall  Mixed  i'und- 
amentals,    while    not    intended  to  be   diagnostic,   have   never- 
theless  been  interpreted   as  being  such  by  many    teachers. 
Form  One   for    instance,    has    ten  addition  examples    scattered 
throughout   the   test.      These   vary   from  simple   examples   such 
as   addition  of   the    simple  combinations    to    the   addition  of 
a   sixteen  number   colvunn,    including  decimal   points.      Others 
of   the    ten   examples    involve    the   addition  of    broken  columns, 
the    addition  of  figures   written   on  a   line    connected   by  a 
plus   sign  and  v hich  must  be  re-written  before    they  are   add- 
ed.     In   fact,    there   are   no   two    examples    that   involve   exact- 
ly  the  same   addition  habits.      Failure  to    do  the   examples    in 
addition   in   this    test  could  not  be   attributed  by  the    teacher 
to  a   single   or   to  even  a    limited  number   of    causes .      Even 
though  the    child   had  a   preponderance   of  erx'ors    in  addition 
examples   of    this   test,    the  teacher  v^ould  not  know   whether 
it  \vas    ignorance   of   combination  or  unfamiliarlty  v/ith   fuch 
a    fcrm  as   2-f  3,    or    inability   to   cope   with  form  such  as    is 
found    in  broken  column  addition,    or   inaccuracy  due    to    the 
necessity   of    re-writing  the  example.      Even   though   the   child 
should  fail   in   the   one   or    two    examples      involving  one    of 
the   above   habits,    the    teacher  could  not  be   certain   that   the 


Page   3 


failure  wan   clue   to  a   disability    that   required   special   drill 
to   overcome   it.      A   test,    in  order   to   be   diagnostic   must  not      | 
only    include    examples   limited   to  a   single    ability,    in  so 
far   as    it    is    possible    to   so   limit   them,    but  there   must  also 
be    sufficient   Instances   of    each   type    of  example  so  that   the 
child   will  have  an   opportunity   to  demonstrate   conclusively 
his    ability   or    inability  to   cope  with  examples      involving  a 
particular  habit. 

V/oody    in  the  Vioody  ■'arithmetic  i^cale  has   devised  a 
test  v;hich  is    more   diagnostic   than   either   of   the   tv/o   that 
have  been    discussed.      But  even   it   cannot   hope   to   give   more 
than   a  general   measur-e    of   power   to   arid,    for    there   are   not 
sufficient   instances  of  each   addition  habit   nor   are    the 
few    of   each  habit    that   do    occur   conveniently   segregated   and 
arranged.      It    included  everything  from  a   simple    combination 
to  the    addition  of  mixed  numbers,    with  about   one   or  two    in- 
stances   of  each   addition  habit.      Even  though   a  teacher  could 
quickly   spot    the  failure  to  perform  the   two  instances   of  one 
operation,   she   could   not   be   certain   that   this    f£iil\are   was   due 
to  anything  but   chance,    for   t'wo   examples    involving  any  parti- 
cular Aritlvnetic  habit  are   not  sufficient    to  measure   con- 
clusively  a  child's   ability   therein. 


Page   4 

Dr.   V/alter   ^.    Monroe    in  his   diagnostic   tests    in 
Arithj-netic  goes   further    than  anyone   else    in  meeting   the 
requirements   of  a   diagnostic   test  namely,    that,    the   speci- 
fic habits   be    isolated   in,    so   far  as   po&sible,    anc   that 
each  be  measured  under   conditions   that  render   comparison 
of   achievements    in  each  test  comparable    with  achievement 
in  any  others. 

Dr.   Monroe   has   sought    to   meet   the   first   require- 
ments by   providing  three   tests    in    the   addition  of   integers: 

(a)  single    column  addition,    three  numbers   high 

(b)  single   column  addition,    thirteen  numbers   high 

(c)  foui'    column  addition,    five  nur.ibers   high 

The   thr^ee    testf-;   given  should  show   v/hether  or    not   a 
pupil's    addition  disability    involves    inaccuracies    dufe    to 
fatigue   or    inaccuracies    due    to    carrying.      Beyond   this    it 
does   not   seem  to  be   diagnostic,      '^here  may   be    other  and  more 
constantly   operative    causes    for    Inability   than  either   of 
those  mentioned.      Such  a   one  miglrit   be    broken   column  form, 
or    inability  to    do    the   combinations    themselves   even  when 
these   are    isolated  and    the   additional  difficulties    incident 
to   the   use   of   them   in  actual    sitviations    in-oerative. 

Concerning  children  who   succeed   in  column  addition 
(five   by  nine)    we   may   of   course    assume    that   they  know    the 
combinations    and   that  they  m8.ke   no  mistakes    in   carrying  but 


Page    5. 


concerning  children   *o   fail    in   this   test  v- e    do   rfot  know 
to  which   of  the   above    causes    to  ascribe    their   inabilitj'^ 
to   add.      Nor   do  we   knov/  whether   blank  spaces    in  some    of 
the    columns,   such  as    occur   in  broken  column  addition  would 
not  be   a  real    obstacle  to  the  pupil.      It  seems   desirable, 
therefore,    to   isolate    each  of    these   habits  even  more    than 
Dr.   Monroe   has   done,    and   to  measure    performance    in  each 
under   comparable    conditions,    so    that  we  may   single    out   the 
cause   of    the   inaccuracy  and  remedy   it. 

Another    point   Dr.   Monroe   has   not   taken   into  account 
fully    is    that   of  reducing  achievements    in    the   different 
habits    to    comparable  units.      Grade   norms   are,    of   course,    in 
a  measure,    such  a   unit.      If  eight  and    six   examples   correct 
are    the    norms    for   a  grade    in  each  test,   respectively,    the 
teacher   can  of   course  compara  roughly    the    achievement   of 
her   class    in   one   test   with   its    achievement    in   the    other  but 
to   the    extent   that  a   pupil   deviates   from  the   average    it  be- 
comes   increasingly  difficult   to  make   an   accurate   comparison 
between  the  accomplishments   of   any   one    pupil   in  two   tests. 
If   a  series    of    tests,    is    to  be   diagnostic  in  a  mot  t  helpful 
way,    it    seems   desirable    that   the    teacher  should    be    able    to 
re(iuce   the    achievements    in   the   several    tests,    particularly 
in   the    case    of    children  that  deviate  most   frojn  the    average, 
to   a   common  denominator. 


Page   6 


Standard  deviation   position   in  a  normal  age   dis- 
tribution woulr]  of  coTarse    furnisb   sucri    a  common  iinit.    The 
difficulty  of  using  such  a   measure   in  the   past  has   been 
that  of  providing  the  teacher  with  the    means   whereby  raw 
scores   can  be   readily   transmuted   into   standard  deviation 
values.      A  part  of   this    study   will   be    the  construction  of 
such  a    table   for  each  of  the    tests  so  that  scores    in   each 
may  be   quickly  transmuted  into  a  common  unit  of  measure 
and  the    teacher  be   enabled   to   compare   directly    the   achieve- 
ments   of   a   child   In  each   test  with  his   achievements    in  any 
other   test  and  thus   locate  his    particular  disability  with 
respect   to  addition-integers. 

The  proposed  tests   aim  to   be    diagnostic  by  virtue 
of: 

1.  Isolating,    in  so   far  as    is    possible,    and  measuring, 
those   habits    in  addition  of   integers   v;hich   seems   to    be    of 
significance    in  the   contribution  which    they  make    to    the 
child's   ability  to    add    integers,      buch  the    following s  eem 
to  be: 

(a)  "•ddition  of   combinations 

(b)  Bridging    the   tens 

(c)  Single    colvunn  addition 

(d)  Addition  with  carrying 

(e)  Cjpoken  coliunn  addition 

2.  Providing  means    whereby  teachers   may  compare  direct- 
ly  the   achievements   of  a   pupil    in  one    test  with  his   achieve- 
ments   in    each   of    the    othf;rs. 


Page   1. 


OUTLINE   OF  PI^OCKDURF: 

I.    Selection   of   examples    - 

By   random  sampllnc   of   single    digits,    and    their 
combinations    into    examples.      This    procedure  was  used   in  ell 
tests   except   the    first,    in  which  case    the   addition  combina- 
tions and  their   reverses  were  used. 

.     II.   Arrangement   of   examples    in  order   of    difficulty   - 

The    relative   difficulty   of    the    examples    was   de- 
termined  by   preliminary   testing  of  grades   three    to   six   in 
tv/o   schools.      Note;    Those   examples,    in   the   case    of  which  a 
high  percentage   of   error  was   due    to   blurred  numbers,    were 
placed  at   the   end  of  each   test.      There   were   nine    such   in- 
stances   in  the   five    tests,    ("ae'    in  test   II;    "h '    in  test   III; 
"g",    "j"    and   "r"    in  test   IV;    "b",    "a",    "g,"    and    "j"    in   test 
V)    pages. 

III.    Giving   of  tests   to  1400    children   in   grades    three 
to   six   inclusive   in  seven   schools    in  Berkeley,    California. 
Instructions    to   teachers   and   tabulation  of   results    are   con- 
tained  on  pages    13-20. 

IV.    Tabulation  of   data   - 

The    zero   scores    in  test   II    that   were   due   to  mis- 
understanding  of   instructions   were   omitted.      Also,    the    re- 
sults   of   the  sixth  grade   of   one    school   were   omitted  because 
a   re-test   shov/ed  first   test   to  have   been   erroneovis . 

V.   Re-testing  of  the   high  third,    high   fourth,    high 
fifth,   and  high  sixth  grades    of   one   school  after   an   inter- 


Page   8. 

val   of   two  weeks    to  get  data   on  reliability   of   test. 
VI.      Statistical   treatment   of   results    - 

1.  Inter-correlation  of   each    test  v;i  th   every 
other   test. 

2.  Correlation  of  each  test  a   second   giving  to 
the   same    children  after    an    interval   of    two    weeks . 

3.  Correlation  with  VJoody-McGall. 

4.  Means   and   standard  deviations   for   each  dis- 
tribution. 

5.  Computation  of   sigma  values   for   each   score 
in  each  test. 


Page    9 


EVALUATING  RESULTS 

VALIDITY  OF  TEST  -   It  has   not  seemed  necessary   to 
gather  evidence  as    to   the   validity  of   the  test  beyond   that 
furnished  by   the    inter-correlations.      They   seem  to   indicate 
that  a  single    type    of   ability    is   being  measured.      They   are 
uniformly  high,    except    in  the   cases    of   test   II   with  other 
tests.      Since    the    correlations    in  which  test   II   plays   a 
part  are    consistently    lov>fer,    and  since   this   test  resulted 
in  an  undue  number  of    zero  scores,    and,    also,   since    its 
self-correlation  was    ].ower   than   the  other   tests,    it    is 
assumed  that    its  validity  as   v/ell    as    its   reliability    is 
lov/   and    it  is   therefore   thrown  out   as    of   little   value. 
The    low  correlation  of   test  V  with  V/oody-McCall    is    inter- 
preted as  being  due    to   the   fact   that  ^''oody-McCall    tests   a 
great  many   abilities    other  than  addition. 

RELIABILITY   -    or   the   degree    to  which   it   is   con- 
sistent  in  its   diagnosis,   would  have  been  determined  by 
checking  one  half   of  the   test  against  the  other  half.      A 
simpler  met?iod   however,    though  a   somewhat   less    satis factorj^ 
one,    was  used,    namely    that   of   correlating   one   giving   of   the 
test   against  another  giving   of  the   same   test.      These   corre- 
lations  were  uniformly   high  except   in   the    case   of    test   II. 
The    latter  v.as   discarded  as   unreliable. 


Page    10 


OBJECTIVITY  -  There  has  been  no  evaluation  made  of 
the  objectivity  either  the  giving  or  the  scoring  of  the  test. 
It  was  sought  to  increase  the  former  as  much  as  possible  by 
simplifying  the  instructions  as  much  as  was  consistent  with 
clear  understanding.  Since  the  instructions  are  not  in  any 
case  complex  it  is  not  thought  that  lack  of  objectivity  of 
giving   is    a    serious   factor. 

Steps    taken   to   insure   objectivity   of   scoring  were 
the   preparation  of  an  an£v;er  sheet   with  answers    so   spaced 
ths-t  they   could  be   placed  directly  under    the    examples   and 
answers   checked. 

In   future  giving  of  the    test    it  is   planned  to   have 
children  score   their    ov;n  papers    since    the   case   of  adminis- 
tration seems    of  greater    importance   than  the   slight   sacri- 
fice   in   objectivity   of   scoring  due    to    the    fact  that  the 
children  do    it.      No  check    was  made   on  the    relative   accuracy 
of   teachers      and  pupils'    scoring. 

SCALING   -   The  examples   were  arranged   in  order   of 
difficulty   by  giving  them  to   300   children   in   grades   tJiree 
to  six    in   two    schools,    each  pupil  having   time    to  work  all. 
In   the    final   form  all   examples   were    included,   arranged    in 
order   of   difficulty  without  any  attempt  being  made   to    select 
only   those   tlriat   represented   equal    increments    of  difficulty. 


Page   11 


RANGE  OF   APPLICABILITY   -    It   was   desired   to   secure 
a   test   which  could  be  used   in  grades   three    to  six   inclusive. 
Reference   to  graphs    on  pages   39-43   and    tables   of  means   and 
standard  deviation   on  pages   45-46   will   show   that  test   I    is 
valuable    in  grades    three    to  sijc    inclusive   though  slightly 
less    so   in  the    latter   two   as  shov/n   by    the   niunber  of  perfect 
scores    made    there.      Test   III   and   IV  easily  measure  grades 
three   to   six.      Test  V  while    it  measures   grades,    four,    five 
and  six   well,    does   not  measure  grade    three.      Therefore  ,    ex- 
cept  for   test   I    in  grade   sir.  and   test  V   in  grade  three    the 
tests   have   a  range   of  applicability   suited   to   these    grades. 

NORlvIS    -   Norms    for   each  test,    in  to    far   as    the    test- 
ing  of    1400   children   in  seven  schools   of   one   school  system, 
can  be    said   to   be  a    basis    for   norms,    are   stated   in    th( 
following  forms  : 

1.  Means    for   each   grade    three    to   six  inclusive. 

2.  Means    for   each  age  eight   to    twelve    inclusive. 

3.  Each  of   the  above   expressed   in   terms   of   a 
Sigma   index    (score  -t-    sigma)    reduced   to  a 
scale    of    1-200. 

Tables   21-30   inclusive  give   value   of  accomplishment 
in  each  test   in   terms    of   sigma.      In   the    last  mentioned   table 
a  score   which  gives  an   equivalent    of   100    is   the   norm  for    the 
age   or  grade   classification  into   v.hich    the   pupil   falls. 
These   norms   are   accurate    only   to   the    extent   that   the   follow- 
ing conditions  hold: 


Page    12 


1.  That   each  dit  tribution  approximates   a  normal  proba- 
bility  curve. 

2.  That   the    reliability   of  each    test  approaches  unity 
as   measured  by  r-epeatin^^  the    tests;    self   correlation      .8   or 
over    for   all   except    test   II. 

3.  That   the   ran£,e   of    the    tests    is    such   as  to  makE    them 
applicable   to    the   group    to   be  measured.      Reference    to   distri- 
bution  tables   7-16    inclusive   shows   that  except  for   test  I    in 
grades    six   and   test  V   in  grade   three    the    tests  do   measure    the 
children. 

4.  That   the   inter-correlation  approach  ninity.    (Accept 

for    correlations  with   test   II    these   are   all  plus   0.8   or  higher. 

USE  OF   TABLC   OF  SIGlJlA 
INDEX  VALUES 

1.   Norm  for   any  sge   or  grade   is   alvyays  such  a   score  as 

will  give   a   Sigma   Index   of    100.    If  a   child's  accomplishment 

in   each  test   is   such  as   to  give   him  a  Sigma   Index  of   IOC    in 

each,   his   scores  are   satisfactory  for  his   age,    assuming   that 

he   is    of   average    intelligence.      If,   however,    he  has  a    sigma 

score   of  80    in  test   IV  and   IOC    in   test   III  his   accomplishment 

in  the   farmer    is   not   as  much  as  we  have   a   right  to   expect 

from  him.      Concerning  each  of    the  tests    in   wlriich  a   child  gets 

a  Sigma   Index  of    less    than   100  v;e   may   say,   v/ithin  the   limits 

of   the   accuracy   of  the    test    that  he    is   not  doing  as    well   as 

he    could  do   in   it. 


Page    14. 

So,    while   this  administration  of  the    test  is   not  for   the 
purpose  of    determininc   the  abilities   of    our   own  pupils    in 
addition  but   rather  as   a  step    iril  the    construction   of  t.   test, 
still   I   believe   that    it  v/ill  be   possible   for   you   to   tell   some- 
thing  from  the   results   as   to    the   type    of  difficulty  which 
should  be  vorked  upon  with  your   own   class    or  with  particular 
pupils.      Do  not  expect   too  much   in  this   respect,   however, 
from  this   preliminary   test. 

DIRECTIONS   FOR    GIVING 
Give    the    tests    in  the   order   indicated   above. 

1.  Distribute    the    first    test,    printed   side  down  on  the 
desk  of   each   child. 

2.  Read   the    following  directions   to   the   children: 

"This    is  a   test   to   see   how    well  you  can   work  addition 
combinations.      V/ork  as   rapidly  as    you  can  until  you  have   fin- 
ished  all   of   them.      I'll   give   you  all  time    to   finish.      V/hen 
you  have   finished   turn  your  paper   over,    printed  side  c'own, 
and  sit  quietly  until   the   others   have   finished.      Now,    turn 
your  pe.pers   over,   v/rite   your  name,    grade   and  date  at   the 
top   of   the    paper  and  go  to   work." 

For   each  of   the   following   tests,    say: 

The   next   is   a   test   in    (insert  name),      ""rite   your 
name,    grade   and    date   at  the    top  of   the   sheet.      V/ork  all   of 
the   examples   and  v/hen  you  have   done    so   turn   yoior   pape  r   over 
and  wait  quietly  for  the  others   to   finish. 

3.  '-'ive  no  help  in  the  working  of  the  examples  except 
to  make  clear  numbers  that  may  be  blurred  or  to  make  clear 
the   directions   above. 

4.  Note   carefully    in  minutes    and    seconds   how   long   it 
takes   each   of    tlie    first   five   and  the    last   one  to    finish. 


Page  13, 


Thousand  Oaks  School. 
Berkeley,  California. 
October  23,  1922. 


II'iSTRUCTlOHS  TO  T5ACHERS  FOR  GIVING  PRISLIMIKARY  TESTS 

Teachers  of  Grades  3,4,5  and  6. 

Please  give  the  following  tests  today,  preferably 
during  the  regular  Ai'ithmetic  period  and  in  place  of  the 
Arithmetic  Lesson. 

1.  Addition  Combinations. 

2.  Bridging  the  Tens. 

3.  Column  Addition  without  carrying. 

4.  Column  Addition  with  carrying. 

5.  Broken  column  Addition. 

This  is  a  preliminary  test  for  the  purpose  of  determin- 
ing the  relative  difficulty  of  the  items  in  each  test.   There 
is, therefore, to  be  no  time  limit  to  the  test,  but  each  cViild 
is  to  work  all  the  examples.   When  the  relative  difficulty  of 
the  elements  has  been  determined  these  will  be  re-arranged  and 
the  final  test  psppared. 

The  purpose  of  the  test,  in  it's  completed  form,  is  to 
help  diagnose  audition  difficulties.   It  should  be  pos?ible 
by  the  use  of  these  tests  to  determine  .just  why  a  class  or  an 
individual  pupil  is  weak  in  addition  so  that  steps  may  be  taken 
to  remedy  the  difficulty.   Later  this  same  step  may  be  taicen 
with  respect  to  difficulties  in  the  other  fundamentals. 


Page   15. 


ADDITIOri  COMINATIOHS 
Name Grade  Date  Right: 


a 

b 

c 

d 

c 

f> 

i-> 

h 

i 

.i 

k 

1 

7    ' 

"     2 

8 

5 

0 

9 

s 

s 

4 

5 

1 

1 

2 

£ 

1 

1 

4 

_1 

2- 

2 

4 

_5 

4 

5 

ri 

n 

0 

P 

q 

r 

o 

t 

u 

V 

IT 

X 

3 

1 

1 

2 

A 

1 

0 

1 

0 

6 

5 

1 

3 

2 

9 

o 

•1 

5 

0 

7 

6 

1 

1 

8 

y z aa         ab          ac  ad  ac          af          a.";  ah ai  a,-] 

1-2              320  4  223  65  2 

6              _3              1           1       -l  1  ±           Z           1  A           ±  9. 

ak     al am an   ao  ap  aq    ar   as  at     au  av 


2 

4 

3 

5 

o 

7 

2 

3 

7 

2 

4 

S 

Z 

i 

_3 

7_ 

^ 

7 

_5 

_2 

0 

_5 

a\,- 

ax 

ay 

az 

ba 

bb 

be 

bd 

bo 

bf 

br. 

bh 

7 

3 

8 

6 

9 

0 

8 

7 

3 

2 

0 

4 

5 

^ 

0 

^ 

^ 

_5 

8 

4 

£ 

± 

7^ 

6 

bi 

b.i 

bk 

bl 

bn 

bn 

bo 

bo 

be, 

br 

bfc 

bt 

9 

4 

8 

5 

a 

2 

4 

6 

6 

9 

9 

7 

3 

8 

_3 

_8 

4 

8 

_9 

4 

S 

0 

4 

7 

bu 

bv 

hm 

bx 

by 

bz 

oa 

cb 

cc 

cd 

cc 

cf 

4 

9 

3 

8 

7 

9 

V 

8 

6 

7 

9 

8 

7 

9 

0 

2^ 

£ 

_7 

8 

7 

£ 

_8 

_9 

Cf. 

ch 

ci 

cj 

ck 

cl 

CI^x 

en 

CO 

cp 

,  ^^ 

-.-• 

9 

5 

9 

8 

q 

5 

5 

S 

8 

7 

6 

6 

5 

5 

6 

8 

9 

7 

9 

7 

5 

8 

^j-'-a 


2 


Nnno 


a. 

14 

+  9  = 

b. 

14 

*  ^  z 

c 

18 

^  4  - 

d 

12 

+  8  = 

e 

19 

*  2  = 

f 

18 

+  8  c 

5 

19 

-^  3  = 

h 

19 

+  9  = 

i 

14 

*   8  - 

3 

13 

+  9  = 

k 

17 

+  7  = 

1 

14 

»  7  - 

BRIDGING 

HE  tva:s 

Page  16, 

■ade 

Date 

y 

19 

* 

RightG 

m 

17 

-♦- 

4  = 

7  : 

n 

19 

♦ 

4  - 

z 

15 

4. 

7  = 

o 

18 

+ 

3  = 

aa 

19 

X 

8  = 

P 

12 

■»• 

9  = 

ab 

19 

4- 

6  s 

q 

16 

4- 

6  M 

ac 

15 

A 

6  * 

r 

13 

4. 

8  = 

ad 

18 

* 

5  = 

wr 

15 

J. 

7  r 

ae 

IS 

* 

5  a 

t 

18 

♦ 

f5  = 

af 

17 

* 

6  » 

u 

17 

* 

9  = 

ag 

15 

J. 

8  = 

V 

16 

+ 

9  - 

ah 

17 

4. 

8  = 

17 

17 

A 

5  = 

ai 

18 

* 

7  m 

X 

15 

* 

9  = 

ak 

19 

18 

X 

5  s 
9  • 

SINGLE  COLUMN  ApDITlON 


Name 

^  Grade  •, 

__  Date 

Right  c 

& 

b 

c 

d 

o 

f 

K 

h 

1 

.1 

k 

1 

4 

1 

8 

2 

8 

1 

9 

9 

4 

1 

1 

4 

3 

5 

6 

6 

1 

4 

6 

4 

S 

1 

8 

5 

6 

8 

6 

6 

2 

7 

4 

1 

6 

8 

2 

5 

6 

8 

3 

6 

4 

Z 

1 

» 

9 

8 

5 

X 

m 

n 

0 

p 

q 

r 

0 

t 

u 

▼ 

■17 

X 

X 

1 

7 

2 

5 

3 

■■■  i 

6 

6 

5 

4 

4 

8 

3 

6 

2 

5 

7 

7 

4 

8 

5 

9 

1 

2 

8 

9 

2 

1 

7 

S 

9 

2 

7 

7 

5 

7 

1 

9 

4 

S 

7 

5 

6 

5 

8 

5 

6 

7 

1 

6 

2 

6 

7 

6 

1 

2 

6 

5 

3 

1 

2 

7 

7 

5 

7 

Xf 


c 
3 


Page 

17. 

• 

- 

BROKEN 

COLUT-N  /DOIT ION 

Nane 

b 

— «i 

c 

u 

&r-do 

'  :.i  b-- 

R 

Right; 
h 

i 

a 

i. 

52 

39 

83 

7 

802 

"86 

8 

5 

572 

St 

602 

1 

983 

82 

1 

8 

66 

68 

73 

43: 

395 

565 

79 

382 

57 

794 

48 

2 

830 

cei 

4- 

83 

99 

372 

467 

4 

987 

757 

79 

39. 

TOl 

580 

63 

527 

44 

347 

962 

69 

68 

Ti 

k 

1 

m 

n 

0 

P 

q 

r 

c 

t 

3 

60 

48 

550 

140 

552 

95 

65 

430 

7 

977 

3 

9 

88 

918 

28 

379 

63 

75 

84 

45 

793 

217 

5 

02 

752 

89 

8 

8 

79 

■  42 

62 

29 

3 

7 

72 

562 

340 

65i 

33 

879 

21 

3 

135 

89 

210 

55 

56 

_Z_ 

Name 


ADDiTIOK  0,'ITH  CARRYING) 
Grade      Date 


Rights 


a 

b 

c 

d 

e 

f 

K 

h 

i 

J 

427 

892 

803 

457' 

108 

295 

432 

249 

512 

717 

158 

992 

247 

205 

494 

857 

202 

789 

875 

9§4 

173 

359 

392 

289 

774 

352 

359 

119 

710 

200 

k 

1 

m 

n 

0 

P 

q  ^ 

r 

G 

t 

534 

221 

101 

846 

375 

855 

364 

501 

898 

G3:-i 

941 

263 

136 

780 

287 

147 

573 

875 

511 

563 

659 

589 

426 

966 

959 

775 

902 

365 

651 

204 

-^^'^ 


p?- 


-  .V 


Page  18, 


T4BLE    1. 


RSSULTS   03?  PRELIMIMARY  TEST  IMG- -AJ^DITION   C  OMBIH.AT  I ONS 
Ex.      Errors        "^x.        Srrora        Ex.        Errors        Ex.        "Plrrors 


a 

1 

aa 

3 

ba 

3 

ca 

19 

B 

0 

ab 

4 

bb 

3 

cb 

10 

0 

2 

ac 

4 

DC 

11 

cc 

13 

d 

1 

ad 

4 

bd 

3 

cd 

14 

t 

5 

as 

2 

be 

3 

CO 

15 

f 

1 

af 

1 

bf 

4 

cf 

20 

& 

5 

as 

2 

bg 

5 

eg 

11 

h 

0 

ah 

3 

bh 

7 

ch 

0 

i 

4 

Ai 

3 

ta 

10 

ci 

10 

J 

1 

aj 

7 

uj 

5 

cj 

14 

k 

3 

ak 

3 

bk 

4 

ck 

18 

1 

6 

al 

3 

bl 

3 

cl 

9 

m 

am 

2 

bia 

4 

cm 

15 

n 

5 

an 

? 

bn      J 

1 

en 

10 

0 

2 

ao 

•» 
o 

bo 

4 

CO 

14 

V 

2 

aP 

3 

bp 

5 

cp 

13 

Q 

3 

aQ 

1 

bq 

3 

cq 

6 

r 

ft 

ar 

2 

br 

9 

S 

e 

as 

4 

b8 

6 

t 

0 

at 

2 

bt 

5 

u 

3 

au 

2 

bu 

7 

Y 

1 

av 

2 

bv 

5 

W 

4 

aw 

2 

bw 

8 

X 

2 

ax 

0 

bx 

2 

y 

3 

ay 

8 

by 

9 

z 

2 

az 

5 

bz 

8 

Pat: 


:!e   ^^. 


TAhLE  2 


INSULTS    G¥   PR-aiMIKARY    TEST liiG— BRIDGING    TTIT!   imiS 


EX. 

No.  of 
Terrors 

FX, 

Ho. of 
Errors 

Ex. 

No.  of 

Hrrore 

Hx. 

No.  of 
"Hlrrors 

a 

30 

i£ 

19 

u 

28 

ae 

38 

b 

29 

1 

20 

V 

30 

af 

21 

c 

18 

m 

18 

w 

16 

e^ 

31 

d 

i;l 

n 

17 

X 

21 

ah 

22 

e 

10 

d 

12 

y 

21 

ni 

21 

f 

iS 

p 

26 

z 

'         25 

aj 

15 

£ 

1    r> 

4.  iil 

si 

24 

fxU. 

28 

ai: 

25 

h 

24 

r 

?7 

sb 

21 

i 

s 

afc 

19 

J 

4L 

t 

50 

ad 

20 

Ex. 

N  0  .  of 
:"rr  or  £ 

^x. 

uO 
T  aB" 

Ko.of 
"terrors 

0 

c 

1. 

■x. 

SlliGLE  COLinai    ATriTIOi^ 

No. of                         No. of 

"rrors       'FSc.        -Errors 

a 

27 

h 

70 

0 

17 

V 

31 

u 

54 

i 

4y 

P 

b3 

w 

29. 

c 

53 

J 

43 

Q 

53 

X 

52 

d 

33 

k 

36 

r 

39 

y 

46 

e 

17 

1 

25 

s 

52 

f 

;i7 

m 

2  b 

t 

39 

.  g. 

39 

n 

40 

u 

57 

Page   20 < 


TABL^i:    4. 


RBbULTb   01'    PRSLlMli4AKY   TE^TIMG— APDITIOli    vVITK   CARKYIIjG 


BX. 


Wo.  of 
ifirrors 


44 


Bx. 


IJo.of 
Srrors 


Ex. 


Ho  .of 
iSrrors 


lux. 


K  o  .  of 
Srrors 


43 


k 


36 


40 


^ 


34 


35 


22 


59 


m 


£^0 


81 


46 


25 


n 


50 


36 


52 


73 


TABLE    5. 


BR0KSI3    CCLUKN   /J)i;iTiOH 


^:x. 

No.  of 

"Errors 

■^. 

Ko.of 

^x. 

KG.  of 

I'lrrors 

■Rx. 

NO.  Of 
^'rrors 

£.-■ 

iOl 

f 

Te- 

yr 

92 

P 

58 

b 

95 

e 

ll? 

1 

77 

1 

79 

c 

96 

h 

68 

m 

51 

r 

fiB 

d 

bi 

i 

y4 

n 

51 

8 

uS 

e 

77 

J 

135 

0 

60 

t 

73 

TABLE    6 . 
i!il>j»..B'".iii   OF    PUriLS   T>J\II>G   ~ACH    7S3T 


GRADE 

Test  I 

Teet  II 

Teet  III 

Test  I\ 

r   Test  V 

TKIRD 

78 

SO 

80 

21 

21 

FOURTH 

74 

68 

74 

73 

73 

FI7Tn 

77 

74 

77 

79 

80 

SIXTH 

87 

89 

88 

87 

R8 

TOTAL 

316 

311 

319 

260 

262 

# 


# 


DIAGNOSTIC  TESTS  IN  ADDITION 
Directions  f-or  giving. 

It  is  very  important  that  the  following  directions  be  care- 
fully followed  if  we  are  to  get  from  the  results  the  hel|>  we 
hope  to  get  in  guiding  children. 

1.  Distribut§  tests,  face  downward.  Warn  children  not  to 
turn  papers  over  until  told  to  do  so. 

2.  Have  them  fill  m  blanks  on  the  back  of  the  test  paper. 
Give  whatever  help  is  necessary  to  insure  an  accurate  record  of 
each  of  the  items. 

3.-  Read  " Instruct ionsTIQ  ^e  f^upils"  aloud,  the  children 
following  silently. 

4.  Note  carefully  the  beginning  time.   It  is  well  to  jot 
it  down  on  a  £iece  of  paper. 

5.  Allow  time  as  follows :- 

Test  1  Addition   Combinations  2  minutes 

Test  2  Bridging  the  tens  2    " 

Test  3  Single  column  addition  2    " 

Test  4  Addition  with  carrying  3    " 

Test  5  Broken  column  addition  3     " 

6.  When  time  is  up  say,  "Stop.   Turn  papers  over." 

7.  Collect  papers. 

SCORING  PAPERS 

1.  Count  "Number  Attempted." 

Jk. .      This  can  be  quickly  done,  since  the  examples  are  ar- 
ranged in  rows  of  10  each.   Take  as  the  number,  the  last  one 
worked,  disregarding  those  skipped. 

2.  Check  with  a  t^       all  answers  that  are  incorrect. 
Ansv;er  sheets  should  be  cut  or  folded  so  th?.t  they  may  be  placed  on 
the  paper  directly  under  the  examples. 

3.  Enter  the  "Number  CORRECT"  in  the  blank  after  RIGHTS  on 
the  back  of  the  test  paper. 

4.  Arrange  the  papers  of  each  test  in  order  of  the  size  of 
score,  the  hSigVjhettsooDce  on  top. 

5.  Fasten  the  papers  of  each  test  together  by  a  clip  or 
a  rubber  band  and  turn  them  in  to  the  Principals  office. 


Page  22. 


11^310135759 
2  2  5  0  7  2  51  1  1 


5627231212 
517  2  339384 


3 

2 

5 

4 

7 

a 

0 

2 

1 

■      4 

4 

7 

2 

5 

3 

2 

4 

2_ 

4 

I- 

0 

1 

3 

6 

5 

4 

5 

3 

9 

0 

6 

6 

6 

3 

4 

2 

3 

7 

2 

5 

7 

8 

3 

6 

4 

3 

2 

0 

4 

3 

4     ■ 

8 

a 

6 

4 

1 

6 

1 

3 

5 

2 

3 

8 

1 

1 

6 

0 

4 

6 

7 

9_ 

3      • 

4 

9 

2 

2 

7 

8 

4 

7 

9 

1 

9 

0 

5 

4 

4 

8 

3 

9 

9 

3 

4 

3 

2 

6 

7 

£ 

0 

7 

6 

9 

7 

5 

9 

8 

9 

6 

8 

:*  9 

S 

0 

6 

9 

3 

5 

5 

9 

8 

6 

6 

7 

7 

8 

8 

9 

5 

5 

7 

8 

7 

5 

9 

6 

7 

8 

7 

8 

8 

9 

?f)^e   as. 


22 


(reverse   side   of  page  } 


AGE  YSAKS kOHTHS 


KO.    ATTEAIPTKD _110.    RIGHT 


GRADE. 
NAME^ 
DATE 


SCHOOL 


INSTRUCTIONS  TO  PUPILS. 

Today  we  are  to  take  five  short  tests  to  see  how  well  we 
can  work  the  different  forms  of  addition.  This  first  test  is 
in  addition  combinations. 

When  I  say  "BEGlli''  turn  your  paper  over,  and  work  as  many 
as  you  can,  being  careful  to  get  them  right.   Stop  work  prompt- 
ly when  i  tell  you  to  do  so.   Ready — Begin. 

TIMB  TWO  KIHUTES. 


Test   1. 


Addition  combinations. 


Page   24. 


1^  4   2 

19    *    3 

18  f    3 

19  I  5 
17  +  5 
IQ    I    4 

16  r+    4 

17  I  4 
17+7 
15    +    6 


14    +    ■?■ 

18+5 
12  +  8 
15+9 
19+7 
19  +  6 
17  +  6 
13+7 
l4  +  8 
17    +    8 


19  +  9 
16    +    6 

16  +  9 
15+7 
12+9 
16+7 
13  +  8 
IS   +    8 

17  +    9 

19  +  a 


14  ^  ^  ■" 

14  +  9  '^ 
16  +  9  = 
19  +  8    = 

15  +  8  = 
10  +  5  = 
13  +  9    i: 


8 

3 

4 

1 

4 

1 

2 

4- 

4 

2 

1 

9 

5 

6 

3 

4 

5 

2 

1 

6 

r^ 

eJ 

4 

5 

2 

6 

7 

7 

1 

7 

6 

4 

6 

1 

3 

6 

2 

5 

6 

1 

6 

5 

7 

4 

7 

2 

3 

1 

7 

7 

1 

1 

1 

8 

6 

6 

7 

1 

4 

6 

8 

5 

8 

8 

4 

5 

2 

1 

6 

8 

3 

8 

2 

4 

2 

7 

X 

8 

6 

7 

9 

8 

3 

1 

8 

6 

7 

8 

9 

5 

2 

4 

6 

6 

5 

1 

6 

9 

3 

3 

5 

8 
.6 

6 
8 
5 


5 
7 
3 
6 
2 


3 

7 
9 
5 
6 


5 
9 
5 
7 
2 


9 
4 
1 
9 
3 


Pe(T«   25, 


(reverse   side   of  page    24  ) 


AGE ^YSARS liCNTHS. 

GRADS 

NASitE 

DATE 


SCHOOL 


NO.    ATTEMPTED 


HIGHT 


IIJSTRJCTIONS   TO   PUPILS  . 
This   is   a  test  to   see  how  well  you  can  work   another  form 
of    addition.      READY— BEGIN  . 

TT5ST   2.      BRiDGlKG   THE   TEUS . 


AGE Y3  -  BS MOiiTIiS_ 

GRADE 

KAltS 

DATE 


SCHOOL 


SO   ATTEMPTED 


RIGHT 


IKSTRUCTIOHS  TC  PUPILS. 
This  is  a  test  to  see  how  well  you  c;  n  work  still  another 
form  of  addition.   READY — BEGIN. 


TEST  3.   SIKGLB  COLUMH  ADDITION 
TIME  TWO  lilNJTES 


Ps&e  26. 


803 

101 

512 

632 

221 

lae 

534 

855 

296 

42'^ 

247 

136 

875 

563 

268 

i94 

041 

14  7 

857 

158 

3  92 

426 

710 

204 

589 

774 

659 

775 

352 

173 

564 

4&7 

8<.6 

892 

511 

24  9 

375 

432 

717 

501 

573 

205 

780 

992 

651 

789 

S87 

202 

954 

875 

902 

289 

666 

359 

898 

119 

959 

359 

200 

356 

48 

530 

552 

430 

140 

£5 

5 

75 

S6 

802 

9 

88 

28 

75 

918 

63 

68 

842 

8 

1 

217 

5 

752 

8 

92 

8 

2 

3 

794 

57 

62 

29 

7 

340 

2 

562 

757 

656 

4 

467 

21 

3 

89 

56 

135 

55 

69 

27 

347 

44 

60 

ik^ 

7 

3 

572 

83 

39 

52 

8 

995 

3 

95 

82 

977 

73 

983 

1 

602 

66 

435 

793 

379 

382 

4  5 

830 

79 

563 

395 

48 

90 

42 

89 

372 

79 

79 

99 

83 

4 

987 

396 

379 

72 

'21Q 

527 

33 

68 

63 

380 

701 

962 

16 

AGS 


Y^ARS 


GRADH. 
DATE 


SCHOOL 


Page  27, 


(reverse  side  of  page  26  ) 


MONTHS 


1^0.  ATTBMPTEH 


NO.  RIGHT 


INSTRUCTIONS  TO  PUPILS. 
This  is  a  test  to  see  how  well  you  can  worK  another  form 
of  addition.   READY— BEGIN  . 
TO  T^ACII'CR  Nate  Change  in  time. 

TBST  4 .   ADI'ITION  WITH  CARRYING 
Time  Tt'iree  minutes 


AGS 


Y15ARS 


MONTHS 


NO.  ATTISMPTED 


NO.  RIGHT 


GR.U)3_ 
NALE__ 
DATS 


SCHOOL 


INSTRUCTIONS  TO  PUPILS. 
THIS  is  a  test  to  see  how  well  you  csn  woric  still  lanotber 
fiorm  of  addition.   READY— JSITG IN. 

TaST  5.  BROKEN  COLUMN  ADDITION 
TIME  THREE  MINUTES 


-  LIaGImOSTIC  7H 

ADDITIOInI  . 

pB^;e  28. 

Tefct  i. 

pombi 

nations. 

4 

5 

6 

0 

8 

5 

10 

8 

6 

10 

10 

7 

9 

9 

10 

6 

10 

5 

9 

6 

7 

9 

7 

9 

10 

10 

4 

3 

5 

5 

6 

7 

9 

9 

9 

6 

8 

10 

11 

5 

• 

11 

16 

11 

12 

8 

4 

8 

1 

7 

8 

11 

11 

12 

13 

3 

8 

7 

12 

10 

14. 

18 

4 

13 

2 

7 

10 

11 

8 

3 

16 

14 

■  9 

13 

14 

12 

13 

14 

15 

16 

15 

13 

12 

16 

14 

15 

17 

12 

13 

15 

17 

Test 

3.  Single 

Column  Addit 

ion 

20 

29 

19 

19 

21 

17 

20 

20 

20 

21 

26 

20 

27 

25 

25 

23 

27 

28 

29 

27 

31 

23 

30 

28 

31 

Test  4. 

Addit 

ion 

With  1 

Garryin 

1078 

1376 

i 

2134 

1777 

1504 

1442 

663 

2097 

1399 

758 

1839 

951 

2292 

2243 

2060 

IIST 

1 

1621 

993 

1871 

1731 

Test  5. 

Broke 

n  Coluran  . 

Addition 

357 

655 

1428 

919 

1287 

753 

901 

1613 

1239 

1371 

17 

1777 

845 

1370 

1137 

1622 

1307 

1066 

1754 

2071 

193: 

Test  2. 

Bridg 

21 
22 

22 
23 
22 
21 
24 
2X 

infi 

the  Ti 

21 
23 
20 
24 

.336 

23 
25 
22 

25 

ens  . 

28 
22 
27 
22 
21 
23 
21 

■  fee 

26 
27 

20 
23 
25 
26 
23 
15 
22 

i:: 


<■  r 


'  •  r 


ts 


Page  29. 


TABLW.  7. 


DISTRIBUTION    OF    SCORES   iiY   GRAD15— ADDITION    COMBINATION 


No*Correct 

*  3d  (irade 

4tVi  Grafie 

5th  Grade 

6th  Grade 

U-o 

a 

4-7 

2 

1 

1 

8-11 

3 

12-15 

1       ' 

16-19 

20-23 

5 

i    2 

24-27 

14 

1 

23-31 

IB 

2 

1 

32-35 

38 

6 

36-3y 

45 

18 

4 

1 

40-4'5 

74 

28 

4 

2 

44-47 

36 

23 

13 

% 

48-51 

41 

34 

12 

4 

52-55 

28 

67 

23 

12 

56-59 

15 

51 

20 

11 

60-63 

7 

51 

33 

24 

'54-67 

7 

3? 

37 

P4 

5S-71 

7 

29 

36 

33 

72-75 

3 

?.5 

51 

43 

76-79 

18 

38 

29 

80-83 

9 

24 

40 

84-87 

8 

15 

14 

88-89 

5 

17 

22 

1    90 

7 

23 

40 

L 

343 

417 

3&4 

5«j3 

Page  SO, 


TABLH  8 


DISTRIBUTIOH  OF  SCORES  BY  GRADE— BRIDGING  TII^  TTSNS 


Iffo. Correct 

3rd  Grade 

4th  Grade 

5'th  Grade 

6th  Grade 

0-1 

?2 

39 

9 

4 

2-3 

14 

8 

0 

0 

4-5 

10 

2 

3 

1 

6-7 

26 

5 

9 

1 

8-9 

29 

8 

0 

2 

10-11 

33 

8 

8 

B 

12-13 

40 

20 

8 

4 

14-15 

38 

35 

13 

4 

16-17 

32 

37 

21 

11 

18-19 

34 

45 

12 

18 

2U-21 

21 

53 

26 

16 

22-23 

9 

32 

28 

21 

,   24-25 

3 

27 

36 

20 

£6-27 

1 

21 

31 

23 

28-29 

2 

14 

34 

32 

30-^1 

0 

13 

27 

15 

32-33 

(> 

9 

8 

25 

34-35 

0 

7 

23 

18 

3e-37 

0 

5 

15 

19 

38-39 

0 

13 

40 

43 

& 

?24 

401 

351 

286 

k 

Pa^je  31, 


?ABLE     9 


DISTRIBUTION   OF    SCORES   BY   GRAD3--SINai^  COLUMN   ADDITION 


No. Correct 

3rd  Grade 

4th  Grade 

5th  Grade 

6th  Grade 

0 

13 

1 

0 

0 

1 

9 

1 

0 

0 

2 

13 

1 

0 

0 

3 

19 

0 

0 

0 

4 

17 

4 

0 

0 

5 

30 

14 

1 

0 

6 

25 

5 

1 

1 

7 

28 

6 

9 

1 

8 

33 

16 

5 

2 

9 

31 

30 

6 

1 

10 

37 

38 

13 

6 

11 

29 

40 

13 

13 

12 

32 

59 

35 

16 

13 

10 

56 

■d'd 

iikJ 

14 

11 

36 

27 

24 

15 

4 

33 

34 

30 

16 

2 

24 

27 

23 

17 

1 

17 

33 

30 

18 

0 

13 

35 

25 

19 

1 

10 

22 

26 

20 

0 

5 

23 

17 

21 

0 

2 

15 

9 

22 

0 

1 

12 

13 

23 

0 

2 

8 

15 

24 

0 

3 

13 

17 

25 

0 

5 

13 

12 

K 

345 

422 

367 

303 

'J;  -I  ■»..  -     iVl  I   ^i  J, 


I    t 


Pac«  '^2, 


-TABLE   IC 


DISTRIBUTION   OF   SCORES   BY  GRAIR-- ADDITION  WITH   CARRYING 


No. correct 

3cl  Grade 

4th  Grade 

5th  Grade 

'  6th  Grade 

0 

26 

10 

1 

1 

14 

1 

2 

25 

2 

3 

26 

4 

2 

2 

" 

4 

33 

10 

7 

1 

5 

63 

15 

1 

4 

6 

43 

33 

7 

2 

7 

34 

42 

15 

13 

8 

37 

58     j     23 

16 

9 

24 

52     i     32 

25 

10 

8 

36 

32 

28 

11 

3 

45     i      54 

36 

12 

7 

38     1     49 

38 

13 

1 

1 
26          42 

39 

14 

12          19 

32 

15 

1 

18          18 

24 

16 

3 

17 

19 

17 

4 

8 

11 

18 

10 

7 

19 

3 

7 

11 

20 

5 

5 

11 

^1  ^ 

344 

417 

345 

319      ^ 

.:[ 


CI 


ex 


li^ 


!t: 


5 


SI 


Page  33, 


TABLE 


i>ISIHI£uTIOB    0?   SCCK^a   2Y  GH.'O}'^ — BPOKT^N   COLUM?    ADDITICM 


Jbio. Correct 

34  Grade 

4th  Gradg 

5tb  Grsade 

6tb  Grade 

0 

116 

la 

2 

1 

48 

13 

2 

2 

Z 

46 

25 

8 

2 

3 

45 

SO 

8 

8 

4 

44 

58 

25 

17 

5 

24 

57 

31 

27 

12 

65 

^y 

37 

1 

4 

54 

54 

50 

8 

43 

58 

41 

9 

4i 

5k; 

10 

16 

37 

32 

ii 

21 

19 

12 

<0 

11 

16 

13 

1 

11 

9 

14 

J      ^ 

4 

14 

15 

1 

1 

13 

16 

3 

12 

17 

1 

2 

^ 

18 

1 

2 

4 

19 

4 

20 

3 

If 

341 

415 

360 

365 

Pa^.;-??  M. 


TABLE 


DISTRIBUTION   OF   SCORES   BY    AOfH— ADDITION 

CCM.BI1U7I0K 

1 

Wo.correct 

.    7 

6 

■      9 

10 

11 

12 

13 

0 

1 

1 

1 

1-4 

2 

1 

1 

5-9 

1 

1 

10-14 

1 

1 

1 

15-19 

20-24 

1 

4 

1 

1 

25-29 

8 

8 

2 

30-34 

3 

18 

13 

8 

1 

35-39 

4 

31 

ii6 

4 

6 

1 

40-44 

3 

50 

1 
40       !      14 

7 

2 

45-49 

2 

28 

29 

16 

10 

o 

2 

50-54 

1 

2S 

44 

55 

22 

10 

1 

55-59 

1 

14 

37 

34 

23 

7 

1 

60-64 

5 

9 

30 

3G 

37 

13 

1 

65-69 

1 

5 

19 

42 

41 

15 

4 

70-74 

10 

22 

55 

45 

21 

5 

75-79 

1 

7 

17 

38 

32 

17 

7 

30-84 

2 

12 

18 

26 

13 

9 

85-09  • 

11 

20 

23 

IS 

9 

90 

7 

17 

25 

25 

7 

S 

S2 

^17 

319 

363 

300 

145 

46 

J 


TABLE      13. 


Ti « ,^  o      '*  *% 


DISTRIBUTION    OF   SCORTi;S   BY   AGTS— BRIDGING   THE    T^.UQ 


-AGE- 

Ixo. Correct 

7  r     8 

9 

10 

11 

12 

13 

0 

10 

24 

16 

9 

2 

1 

3 

3 

1 

ii-3 

8 

8 

3 

4-5 

3 

5 

3 

5 

e.7 

1 

13 

14 

2 

3 

1 

8.9 

1 

19 

6 

5 

2 

1 

lu-ll 

4 

14 

15 

11 

11 

1 

12-i-? 

2 

26 

17 

8 

11 

1 

. 

14-15 

1 

24 

21 

17 

9 

4 

' 

16^17 

4 

25 

21 

27 

lb 

2 

1 

itt-iy 

21 

32 

19 

■^l 

6 

>0-?l 

3 

19 

33 

31 

10 

7 

3 

22-23 

11 

17 

22 

33 

10 

' 

24-25 

1 

21 

31 

18 

9 

4 

iJ6-27 

1 

3 

12 

ki5 

23 

a 

3 

p.a-29 

4 

12 

25 

S9 

11 

29 

•■^0-31 

1 

5 

21 

18 

6 

3 

32-33 

2 

9 

12 

18 

5 

2 

34-35 

1 

10 

13 

15 

7 

1    ^ 

36 

2 

5 

8 

5 

7 

3 

37 

1 

15 

34 

33 

27 

12 

H 

19 

211  1 

303 

333 

288 

113 

i   72 

^"i 


I     / 


# 


\^^3    36. 


TABLTi:     14, 


UibTRliiUTlOll   Oi"-   SCORES  BY   AGE— o.l.GLH  COL^r-i:   ATT^T.CK 


- 

So. Correct 

7 

b 

i# 

xu 

11 

13 

0 

a 

5 

1 

1 

to 

5 

1 

2-3 

16 

tt 

3 

4*5 

k, 

ii4 

ly 

D 

<• 

6-7 

4 

50 

13 

13 

2 

3-9 

2 

4«; 

oy 

15 

13 

4 

iU-11 

b 

^9 

(iw 

42 

23 

7 

12-13 

i 

.^'J 

65 

81 

44 

16 

5 

?.4.15 

1 

17 

47 

57 

51 

16 

9 

ir,-i7 

4 

>] 

48 

54 

5 

16-3  9 

££: 

44 

38 

24 

7 

20-21 

1 

9 

24 

r.l 

13 

■» 
t 

i:;j-ir3 

1 

5 

11 

14 

17 

7 

24 

y 

^0 

8 

C 

2 

2b 

1 

16 

11 

7 

£i 

17 

^j:;6 

v.i;to 

5  0  5 

296 

io5 

48 

-?) 


PatTe  ^B, 


TABLE    16. 


DISTRIBUTION   OF   SCORES   BY    AGS— BR0KJ5N   COLUMN    ADDITION 


-AG 

S- 

No.  Correct 

7 

a 

9 

10 

11 

12 

iS 

0 

5 

58 

39 

11 

2 

1 

4 

25 

8 

7 

5 

2 

2-3 

4 

58 

45 

25 

14 

6 

2 

4-5 

5 

44 

64 

83 

46 

15 

8 

6-7 

1 

20 

74 

91 

75 

28 

9 

8.9 

12 

49 

73 

81 

30 

7 

10-11 

2 

18 

43 

43 

19 

7 

12-13 

1 

4 

13 

13 

16 

4 

14-15 

1 

i 

4 

5 

12 

7 

4 

16-17 

1 

6 

2 

7 

4 

18-19 

2 

3 

3   1 

4 

20 

\ 

2   , 

2 

H    ^- 

19 

221 

308 

360 

298 

134 

47 

' 

?«ge    *S9. 


ADDITIOM   COMBIl^ATIONS. 


uH  ■ 


3^ 


/& 


6th  Grade. 


^S 


?i^ 


/(^ 


^^ 


>^2J 


^T- 


/4 


■ 

31 


5th  Grade. 


/      r 


4th  Grade. 


^ 


I      > 


3rd  Grade. 


"  '\       J'     '» ^C' — ^t" — i '  »^"  ""» T' — t"  ■■■  ■% ) r- — -1 ]i r r — t h •  ■      >»'       •      '  J 


rn. 


if/,     /V    'Y  X3  Z7  3/    3s   3 


1      f3     *7      -i/     -i'S  -ij    6  J      0?    ?/     To'    "7/     ^3     8-f     ■*o 


4.         3 


J3R1DGOG   THE   T3NS. 


Pai;e  40. 


6th  Grade. 


J — '- 


Sth  Grade. 


n 


4th  Grade. 


^^ 


J?6 


3rd  Grade. 


/      3     3r     7      ^     ^7     o     O-    />    /^     2/    ^J   ;^J'  2/  2?  3/    3J'  37     3^ 


.i> 


J<o 


X'f- 


/2- 


34. 


2Vf 


IX. 


3i- 

II-   - 


Pa^e   41. 


SINGLE  COLUMN    ADDITION. 


6th  Grade. 


._J 


5th  Grade. 


n 


Lr 


4th  Grade. 


r 


n 


j4 


a-/-  ■ 


12. 


3rd  Grade. 


1 1 — T II  I         «  ^ « •  i'  f T !1 J—'. !  S       '    , 

■J-      3       "/      >>       6        7      5^      ?      ^o      //     ^1-     '3     'V    /J-    y^     />    'f     /9     2<j     3y     22.    23    2^      :i 


^  r  r^ 


3<" 

-J-7 


ADDITION  WITH  CARRYING 


6th  Grade. 


r,t;e  42. 


A       / 


3-      J         ^       J        t 


7      S      <f     /o     //     ,  >_  li    y/     'i'  /(,     '?    'i'   ''>    yjiJ 


-^4 


91' 

1% 


H^ 

^ 

ra^e   43. 

Jt 

1 

BROKEN   COLIMN   ADDITION. 

>-J 

si 

6th  Grade. 

f 

r 

-^ 

0 

I — '                                     >— 1 

^ 

_n 

i/y 

- 

36 

. 

' 1 

5th  Grade. 

%1 

- 

WV^I«. 

/f 

' 

1 1 

r 

I 

'                       S_-^_ 

1 

.>^ 

1 s-^ 

tt--^' 

- 

Jt 

• 

4th  Grade. 

7'' 

- 

.         x 

/X 

— . 

' 

f 

1 

— 

J 

L-u-j—i        ,   . 

p 

«   .    , 

»                     V 

3       ^ 

^     s 

-    C 

7 

J^ 

^ 

/ 

D 

'■       /- 

(,     ^5      .  V      1  y     /  fe     / 

->    '  >     >  f  i.  • 

3rd  Grade. 


1 » r 


/      ;?.    3     y.    or    (6      7     F      f    /<•      'f    t  i,   «i     t)^  /-J^  /fe     /y  /*    /y  ^< 


Page  45. 


CO 

« 

to 


CM 


oo 

« 
CM 


o 

CM 


s 

^ 


CO 

o 

E-' 

cq 

H 


O 
I 

I 

CO 

2; 
o 

M 

I 


CO 

CO 


)Si 


t 
CO 


00 


CO 


CO 


C3 


in 


CM 
00 


C5» 

to 

« 

to 


o 


to 

CM 

f-4 


10 

to 


to 


CO 

r-l 


U3 


CM 

• 

CO 


to 

• 

CM 


10 

M 

H 


CM 

CO 


<o 


en 

CM 


CJ» 


m 


o 

CM 

to 


i 

to 


C3» 
00 


'if 
to 


CM 


to 


CM 
0» 


vO 
O 

CJ» 


«o 

to 


o 

10 


H 
CM 


in 

CO 

CM 


in 


00 

to 


CO 

CM 

• 
CO 


lO 

«o 


CM 

"00" 
O 


<o 

at 

CM 


to 


Page  47. 


TABLl?      21 , 


SIGMA   II^DEX  VALinSS   Y'On  SCO'llSS   I*i    ?y;ST    I. 


•^ 

-  Aaii;- 

'''•■- 

1 

B6ore 

8  yrs 

^   .-— .  » ... 
9  yrs 

10  yrs 

11  yra 

f         '  ■■ 

12  yrs 

5 

36 

37 

21 

9 

10 

46 

43 

28 

16 

7 

15 

53 

50       ; 

34 

•dS 

15 

20 

60 

56 

41 

30 

22 

25 

68 

62 

48 

37 

29 

30 

75 

68 

54 

44 

36 

35 

83 

74 

61 

51 

44 

40 

90 

80 

67 

h8 

51 

45 

97 

87 

74 

65 

58 

50 

105 

93 

81 

71 

ee 

55 

112 

99 

87 

78 

73 

60 

120 

105 

94 

85 

80 

65 

127 

HI 

101 

92 

88 

70 

135 

117 

107 

99 

95 

75 

142 

124 

114 

106 

102 

80 

149 

130 

120 

113 

110 

65 

157 

136 

1.27 

120 

117 

90 

164 

142 

134 

127 

124 

1.482 

1.224 

1.324 

1.334 

1.462 

liOTE   -   to  find  Sigaa  Index  Values   for   intermediate  points 
add   amount    on   line    (#)    to   the  value   of   the  next   lower   score 
above   for  each   unit    of    score.    3X.    36=   83  plus   1.482   or   84.482 
37=    83  plus   2x1.482   or   85.96 


Pe^e  48. 


T.^iiLE    22. 


SIGJ».A  IhHrX  V A^ UIl;£  iCn   scons   J^  ':'EST    II. 


r                                      -AGS- 

Score 

8  yrs. 

9  yrs. 

10  yrs. 

11  yre. 

12  yrs. 

2 

66 

67 

55 

51 

29 

4 

71 

70 

59 

55 

35 

6 

77 

75 

64 

eo 

40 

8  • 

82 

7:, 

68 

64 

45 

10 

a  7 

S3 

72 

68 

51 

12 

93 

86 

76 

73 

56 

14 

m 

90 

80 

77 

61 

16 

— 
103 

94 

85 

81 

66 

18 

109 

96 

89 

86 

72 

20     114 

102 

93 

90 

77 

22     119 

106 

97 

94 

82 

24      125 

110 

1-01 

99 

88 

26     130 

114 

135 

103 

93 

23 

13G 

110 

110 

107 

98 

30 

141 

122 

114 

112 

104 

32 

146 

126 

113 

116 

110 

~34 
36 

152 
157 

130 

122 

120 

114 

134 

126 

125 

120 

38 

162 

13B 

131 

129 

125 

if 

2.688 

1.984 

2.096 

2.164 

2.659 

NCTS  -   to  find  Sigma  Index  Valu«8  for  intermediate  points   add 
atiount    on  line    (#)   to  the  value    of   the  next    lower   score   in  t'le 
first   column   above.     ;x.    Score   27   =    120   dIus   2.688*132.688   or 
133. 


f^e,*^    49. 


TABLS     23 . 


SIQMA  lj;i3gX  VAlUaS  FOR  SCOKIa   Ilj    TEST   III 


-Aa.g- 


Scor« 


8  yrsi 


68 


9  yrs. 


56 


10  yrs^ 


45 


11  yra. 


30 


1£  yrs, 


oo 


77 


64 


o4 


39 


»3o 


6 


86 


73 


62 


4G 


47 


6 


95 


81 


70 


57 


55 


10 


104 


89 


76 


64 


12 


113 


97 


66 


(V 


14 


122 


105 


94 


84 


81 


16 


131 


113 


103 


94 


90 


18 


140 


122 


111 


103 


99 


20 


149 


130 


119 


112 


107 


22 


158 


136 


127 


121 


116 


24 


167 


146 


135 


628 


4.081 


4.081 


4.540 


4.O'*0 


aOT-'^  ..    bo  find  Sifc.flia  Index  Values   for  interiiiedii.te  pointj 
add  amount    on   line    {Ir)    to  the  value   of   the  next   lower   score 
in  the   rirst   cclusji  ^ccve.      £x.   ii^covfi  23-   15o  piu&  4.C2G 
or  162.628 


Pa.;e   50. 


TaBLH;    24. 


SIGLA   IIJIIDC  VALU'-S   T  01^   SCOI'J^S    IK    TTEST   IV 


1 

Score   B  yrs.    9  yrs. 

10  yrE. 

11  yrs 

12  yrs. 

1 

67 

59 

47 

20 

36 

73 

64 

52 

36 

41 

3 

78 

69 

57 

42 

.4fi 

4 

t4 

74 

63 

48 

fiS 

5 

90 

79 

63 

54 

fi7 

6 

95 

83 

73 

61 

f^9 

7 

101 

88 

78 

67 

fi7 

S 

106 

93 

S4 

73 

7a 

9 

112 

98 

£9 

79 

7fl 

10 

lis 

103 

94 

86 

R.-^ 

11 

i;i5 

103 

';;9 

02 

rtH 

12 

li39 

113 

105 

94 

13 

134 

117 

110 

104 

Q9 

14 

14^ 

1^-: 

115 

111 

104 

15 

146 

127 

120 

117 

ino 

16 

151 

132 

126 

123 

lift 

17 

157 

137 

131 

129 

ion 

13 

162 

142 

136 

136 

iy.fi 

19 

icS 

14c 

142 

142 

20 

174 

151 

147 

148 

T  'J  /-• 

# 

3.58 

4.12 

3.8 

3.2 

— 6»a6   i 

Fa^:»    ?>1. 


TABLS    25 


SIGaA  INET^i  VALJt-L:   _?<!!>   SC^:  PrS    IK   ?5ST  Y. 


Score 


8    yrfei 


9    /rs 


10  vrs, 


11   yrg, 


la  yrf 


2 


A 


6 


8 


10 


11 


12 


13 


-  14 


15 


16 


le 


Id 


20 


M^ 


92 


Jti'JL 


ice 


X'iU 


1^8 


1&6 


164 


172 


IflO 


LIS 


I9e 


S.QO 


65 


100 


106 


liJ 


116 


124 


iro 


IZG 


14; 


14  6 


It  a 


U5 


IVl 


1''7 


183 


5.S82 


65 


7X 


7<> 


83 


31. 

92 


9B 


103 


108 


114 


iiy 


li-4 


i.'^.y 


I'b 


141 


146 


IM 


157 


If.? 


168 


5.376 


57 


63 


69 


74 


30 


36 


38 


104 


110 


llf 


igs 

127 


l?,y< 


\7,9 


145 


151 


157 


16? 


166 


5.882 


60 


66 


71 


76 


ei 


S7 


QO 


97 

102 


107 


113 


118 


1J:3 


129 


1.^)4 


139 


145 


l^C 


•155  • 


5.262 


Pag4   52, 


7ABLB   26. 


SIGKA   INDISX  VM-U^'IS   FOR    SrQRBS    IN    TCST    I. 


-GHADT5- 

Score 

Third 

Fourth 

:"ifth 

i:ixth 

< 

30 

20 

11 

10 

39 

28 

18 

15 

48 

35 

26 

4 

20 

57 

43 

32 

12 

25 

67 

50 

39 

20 

30 

76 

57 

46 

28 

35 

85 

65 

63 

36 

40 

95 

72 

60 

44 

45 

104 

79 

66 

52 

50 

113 

87 

73 

60 

55 

122 

94 

80 

68 

60 

132 

101 

87 

76 

65 

141 

109 

94 

84 

70 

150 

116 

101 

92 

75 

159 

123 

108 

100 

80 

169 

131 

115 

108 

85 

178 

138 

122 

116 

90 

187 

145 

129 

124 

i 

1.851 

1-470 

■  "  •'       ■ 

1,388 

1,6 

hOTK  -  to  find  Sigma  index  Values  for  intermediate   points   add 
amount   on  line    (#)    to  the  value   oi    the  m-xt   lower   score   in  thft 
first   column  above.    ICx.    ii^ore  27=    67  plus    (2  x   1.851)    or   70.702 


4, 


--> 


i  c 


Page  55, 


TABLE    27, 


SIGMA  INDEX  VALUTAS  POR  SCOR-RS    IfJ    Tp^K?    II. 


-GRADE- 

Score 

Third 

Fourth 

Fifth 

bixth 

2 

67 

63 

52 

37 

4 

73 

67 

56 

42 

6 

80 

72 

60 

47 

8 

86 

76 

64 

52 

10 

92 

80 

68 

56 

12 

99 

85 

72 

61 

14 

105 

89 

76 

66 

16 

111 

93 

80 

71 

18 

118 

98 

84 

76 

20 

124 

102 

88 

81 

22 

130 

106 

92 

86 

24 

137 

111 

96 

91 

26 

143 

115 

100 

96 

28 

150 

119 

104 

101 

30 

156 

124 

108 

106 

32 

162 

128 

112 

111 

34 

169 

132 

116 

116 

36 

175 

137 

120 

121 

# 

-.,.3.i74 

iLill^ 

2<02  , 

2.4«a 

IilOTS  -   to  find  Sigma  index  Values  for  intermediate  pointe   add 
amount    on   line    (#)    to  the   value   of   the  n-xt   lower   score   in   the 
first   column   above,   ifix.    Score   27-143  plus  3.174   or  146.174 


Pai^o   54. 


TaBLB     28. 


SIGliA  IhlQ-'^X  VaLuKS  FOB   SCORi;S    IK    TKSY    IH 


-GRAX*'^- 

Score 

Third 

yourth 

Firth 

Bixtta 

1 

62 

36 

'^<■J 

15 

2 

67 

44 

33 

20 

3 

72 

49 

38 

25 

4 

77 

54 

42 

30 

S 

83 

59 

47 

35 

6 

88 

64 

51 

40 

7 

93 

69 

56 

45 

8 

99 

74 

61 

50 

^ 

104 

7y 

66 

55 

10 

-  109 

84 

70 

61 

11 

114 

89 

74 

66 

12 

120 

94 

79 

71 

13 

125 

99 

83 

76 

14 

130 

104 

88 

81 

15 

135 

110 

92 

36 

16 

141 

115 

97 

91 

17 

146 

120 

102 

96 

16 

151 

125 

106 

101 

19 

156 

130 

111 

106 

20 

162 

135 

115 

111 

21 

167 

140 

120 

116 

5.263 


5.076 


4.558 


5.063 


TABLE    29. 


Page   55, 


SIGMA  IHDEX  VA  in?;S   FOP   SCORES    IN   TI^ST   IV. 


T 

-GRAD15- 

Score 

Third 

Fourth 

Fifth 

Sixth 

1 

64 

50 

33 

31 

2 

71 

56 

39 

37 

3 

79 

61 

45 

43 

4 

87 

67 

51 

48 

5 

95 

72 

57 

54 

6 

102 

78 

63 

60 

7 

110 

84 

69 

66 

6 

118 

89 

75 

71 

9 

125 

95 

80 

77 

10 

133 

101 

86 

83 

11 

141 

106 

92 

89 

12 

149 

112 

98 

94 

13 

156 

118 

104 

100 

14 

164 

123 

110 

106 

15 

172 

129 

116 

112 

16 

179 

134 

122 

117 

17 

187 

140 

128 

123 

18 

195 

146 

134 

129 

19 

151 

139 

135 

20 

157 

145 

141 

,  # 

7.718 

5.632 

5.898 

5.762 

P8m:;s    56. 
TABLE       30. 
SIGMA  Il'JDBX  VALUl^S   FOR   SCCRSS    Hi    T^ST  V  . 


-GRADE- 

Scor« 

Third 

Fourth 

i'ifth 

Sixth 

1 

85 

63 

51 

55 

2 

95 

70 

58 

ei 

3 

105 

77 

65 

66 

4 

115 

84 

71 

71 

5 

125 

91 

78 

76 

6 

135 

99 

85 

32 

7 

145 

106 

92 

87 

8 

154 

113 

99 

92 

9 

164 

120 

105 

97 

10 

174 

127 

112 

103 

11 

154 

134 

119 

108 

12 

194 

141 

126 

113 

13 

149 

133 

118 

14 

157 

140 

124 

15 

163 

146 

1£9 

16 

170 

153 

134 

17 

177 

160 

139 

18 

184 

166 

145 

19 

191 

174 

150 

20 

199 

181 

155 

#< 

9.92 

7.142 

6.826 

5.262 

ONE  MONTH  USE 

PLEASE  RETURN  TO  DESK 
FROM  WHICH  BORROWED 

EDUCATION-PSYCHOLOGY 
LIBRARY 

This  book  is  due  on  the  last  date  stamped  below,  or 

on  the  date  to  which  renewed. 

l-month  loans  may  be  renewed  by  calling  642-4209 

Renewals  and  recharges  may  be  made  4  days  prior 

to  due  date. 

ALL  BOOKS  ARE  SUBJECT  TO  RECALL  7  DAYS 

AFTER  DATE  CHECKED  OUT. 


m 


LD  21A-30m-5,'75 
(S5877L) 


General  Library 

University  of  California 

Berkeley 


